Cusp
From Encyclopedia of Mathematics
ordinary cusp
A singular point of specific type of an algebraic curve. Namely, a singular point of an algebraic curve
over an algebraically closed field
is called a cusp if the completion of its local ring
is isomorphic to the completion of the local ring of the plane algebraic curve
at the origin.
Comments
A cusp can also be defined via the so-called intersection number of two plane curves at a point, cf. [a1], pp. 74-82. A generalization of a cusp is a hypercusp, cf. [a1], p. 82.
References
[a1] | W. Fulton, "Algebraic curves. An introduction to algebraic geometry" , Benjamin (1969) pp. 66 |
How to Cite This Entry:
Cusp. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cusp&oldid=23804
Cusp. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cusp&oldid=23804